The Nature of Inorganic Solute Species in Water - Advances in

8 The Nature of Inorganic Solute Species in Water 1

S. Y. TYREE, JR. Downloaded by CORNELL UNIV on May 27, 2017 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/ba-1967-0067.ch008

University of North Carolina, Chapel Hill, N. C.

In the range of pH exhibited by most natural water and in the concentration range greater than millimolar few metal ions exist as simple hydrated

cations, and relatively

few

oxyanions exist as simple monomeric species. The hydrated cations are good buffers toward bases, the metallate ions toward acids. As pH is raised in solutions of many hydrated cations, isopolycations are produced,

and ultimately,

hy-

drous metal oxides precipitate. As pH is lowered in solutions of many metallate ions, isopolyanions are produced, and ultimately, hydrous oxides precipitate.

Salts of the inter-

mediate isopolyions precipitate in some cases. Where the results are unambiguous, the nature of the species can be described.

intermediate

Kinetics are thought to have been

neglected in studies of such solutions up to the present time.

In the past 20 years several physical inorganic chemistry laboratories have re-examined extensively the nature of the "simple" inorganic solutes in water. Substantial contributions to man's knowledge of the hydrolytic behavior of metal cations and metallate anions in water solvent have resulted. Various new techniques have been applied with varying degrees of efficacy. The details of the behavior, within specified conditions, of a number of solute ions are now matters of fact. In many more cases and over wider variations of conditions, all of the important variables which affect hydrolysis phenomena have not yet been identified. We will attempt to describe broad areas of general agreement, list and comment briefly upon the techniques which have been employed, present in detail what is known of one or two solute systems within 1

Present address: College of William and Mary, Williamsburg, Va. 183 Stumm; Equilibrium Concepts in Natural Water Systems Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

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narrow conditions, summarize—using specific examples—the variables considered important in hydrolysis phenomena, and consider the extrapolation to natural water chemistry. N o attempt is made to survey comprehensively the state of knowledge of the hydrolytic behavior of all metal cations and metallate anions in water. Further the reader must bear in mind that most of the work done by physical inorganic chemists in this field has been done on solutions of metal solute concentrations greater than millimolar.

Downloaded by CORNELL UNIV on May 27, 2017 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/ba-1967-0067.ch008

General Agreement Metal cations, Me" , with the square root of ionic potential (7), y/ , less than 3.2 exist as simple hydrated cations, [ M e ( O H ) „ ] " \ only at low pH—i.e., 1 or 2. As the p H of such solutions is raised, the hydrated cations are converted into isopolycations, [ M e ( O H ) ( O H ) „ ] ~ * . ( From here on, waters of hydration w i l l not be included in formulas since in most cases the numbers are not well established. In other words, M e ( O H ) „ " w i l l be abbreviated as M e " and [ M e ( O H ) ( O H ) „ ] ] - , exhibits a p H of 2.23. When an additional 0.060 mole per liter of N a C 0 is added to the solution, vigorous effervescence is observed, and the p H is raised to only 2.46. Clearly the base is bound by the gallium-containing cations, resulting in an "average" solute cation (36) of [ G a ( O H ) i . ] . Ultimately as more base is added to solutions of isopolycations, hydrous oxides or salts of isopolycations separate as heterogeneous solid phases. Elements of y/ greater than 3.2 form simple metallate anions in solutions of high pH—i.e., strongly alkaline solutions. As the p H of such solutions is lowered, isopolyanions are produced in many cases, ultimately yielding hydrous oxides, or salts of isopolymetallate ions as heterogeneous solid phases. Again, many of the isopolyanions exhibit buffer capacity. A few metal ions—e.g., gallium (III) ion, aluminum ion, tin (II) ion, in general those metal ions which have been described as amphoteric— are able to form both isopolycations and isopolyanions. 3 +

0

L

5

2

7r,+

2

3

7 5

1 2 r , +

Techniques Used Most of the techniques evolved by workers investigating the nature of electrolytic solutions from 1900-1950 have been applied, with varying degrees of success, in studying aqueous ion hydrolytic phenomena. In

Stumm; Equilibrium Concepts in Natural Water Systems Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

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Inorganic Solute Species

addition the physical techniques of the organic polymer chemists have been used. Potentiometrie Titration. This is probably the simplest and most straightforward way to detect aggregation coincident with hydrolysis. In practice the p H change in a solution of a given metal ion is followed carefully as base (or acid) is added, keeping the ionic strength of the solution high and constant (2 or 3 M N a C 1 0 or L i C 1 0 ) and keeping the total metal ion solute constant. A family of such titrations over as wide a range of total metal solute concentrations as possible is obtained. In those cases where a reversible metal ion indicating electrode is known, the changes in unhydrolyzed metal ion are followed simultaneously with p H measurement. The supporting electrolyte minimizes the effect of changes in ionic strength on measured values of e.m.f. A short, yet adequate description of the treatment of the data is given by Sillén (39). At best, equilibrium constants relating solute hydrolysis products and the hydrated ion precursor can be obtained. A t worst the average solute stoichiometry can be obtained, which is a necessary preliminary to several of the other techniques to be discussed. In general precise, reproducible data cannot be obtained from solutions containing less than a millimolar total metal solute. The most effective proponent and practitioner of the technique has been Sillén. Contributions from him and his many co-workers in Stockholm are clearly more numerous than those from any other group studying inorganic hydrolysis in the past 15 years (39). Partition Chromatography. Liquid-liquid extraction and ion-exchange techniques have both been used to infer the nature of cationic and anionic species. In both techniques, the ionic species are partitioned between two phases. The mass and/or charge balance permits one to determine solute charge from batch equilibration experiments alone. If the solute species are of several kinds, chromatograms w i l l separate the species into fractions. In interpreting the experimental data, one must assume that the solute species cross phase boundaries unchanged. In my opinion the foregoing assumption has not always been justified. A n unambiguous example of determining the charge on a polymeric cation by the ion-exchange method is the work of Ardon and Plane (3) on [ C r ( O H ) ] . Using radioactive tracer metal ions, these techniques have been used in total metal concentrations as low as micromolar (34). Crystal Analysis. Of course, the elemental and crystal structure analyses of crystals obtained from solutions have been used to infer structures of ionic solute precursors. Thus, Lindqvist's x-ray crystal structure analysis of ( N H ) M o 0 * 4 H 0 shows that the crystals contain the structural unit, M o 0 ~ . Lindqvist also showed that the solutions from which the crystals are grown do contain essentially monodis-


4

2

2

4

4 +

4

6

7

7

2 4

2 4

2

6


186

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WATER

SYSTEMS

Sillens

perse heptamolybdate anions (23). O n the other hand early work on B i ( I I I ) was interpreted in terms of a polydisperse series of isopolycations (14) [Bi„ i O „ ] < which were considered as possible precursors of the ( B i O ) „ sheets found in the crystal structures of some bismuth oxide halides. Subsequently one of Sillens associates, Olin, found that, within limits, the solute hydrolysis product of B i is essentially monodispersed [ B i ( O H ) ] ion. Aveston and Johnson (5) report that the Raman spectra of crystals of K T a O i 9 ' 16 H 0 and of saturated solutions of the crystals are the same. The light-scattering and ultracentrifuge techniques agree on the identification of the solute isopolyanion, Ta ;Oi ". Under this category of techniques it should be noted that one is able to achieve identification of principle species only. Diffusion. The rate of self-diffusion of a metal solute species has been used to infer the degree of aggregation of the solute species, in accordance with the postulate that the diffusion coefficient is inversely proportional to the square root of the ionic weight of the solute. A n example is the study of isopolytungstates by Anderson and Saddington ( 1 ). However, Baker and Pope ( 6 ) showed that two heteropolyions, of essentially the same structure, yet differing in ionic weight by about 1000 units, have essentially the same diffusion coefficients. Thus the interpretation of diffusion data in most cases needs to be reconsidered. n+3)+

+

?

3 +

6

8

i 2

f > +

2

6


(

9

8

Spectrophotometry. In general the edge of continuous absorption (charge transfer spectra) for solutions of both metal cations and metallate anions undergoes a red shift coincident with isopolyion formation. As well, the d-d spectra of transition metal ions are shifted by isopolyion formation (not always a red shift in this case). In optimum cases, equilibrium constants relating the parent solute ion and the hydrolysis product solute ions can be obtained. The work of M i l b u r n and Vosburgh (28) on the F e hydrolysis is an excellent example. 3+

Cryoscopy. Souchay (40) has summarized the application of fused salt cryoscopy to ionic solutes. Obviously two limitations are inherent in this method. Under ordinary pressures, measurements are possible at only one temperature—namely that of the transition point (e.g., ca. 32.38°C. in the case of N a S 0 • 10 H 0 ) . Secondly, the solute is being examined i n "solutions" of high ionic strength only. Isopiestic vapor pressure measurements have been used as a variation, which, in principle, eliminate both limitations. However, it does not appear that it is as yet possible to analyze such data to yield equilibrium constants (33). Furthermore, Tobias has cast doubt upon the inherent accuracy of the method when the polyions contain more than 3 or 4 metal ions (41). 2

4

2

Intrinsic Viscosity, Ultracentrifugation, and Light Scattering. These three techniques have been used extensively by workers investi-



8.

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gating the properties of organic polymers and organic polyelectrolytes. Their use in studies of inorganic hydrolytic solutes has been much less extensive. By analyzing the variation of solution viscosity with solute concentration, it is possible to estimate several properties of a solute— e.g., degree of aggregation and magnitude of charge. In studies of inorganic hydrolytic phenomena this method has been essentially limited to phosphate and silicate solutions. A good review of these areas has been included in Gimblett's recent book (13). Kraus et al. ( 19 ) have shown that sedimentation profiles of solutions which have been centrifuged (10,000-25,000 r.p.m.) to equilibrium can be analyzed to yield good estimates of the degree of aggregation of the solute metal ion hydrolysis aggregates, a measure of the degree of polydispersity of hydrolysis products, and an estimate of the charge on the solute species. M a n y cation and anion hydrolysis systems have been investigated by this technique. A n excellent example is the recent work of Hentz and Johnson on thorium solutions (15). Debye and Naumann first showed that Rayleigh scattering could be used to estimate the molecular weight of low molecular weight solutes in aqueous solution (9). Since then the technique has been used to estimate the degree of aggregation in solute metal hydrolysis products for many cation and anion systems (42). A recent example is the study of thorium reported by Hentz and Tyree (16). The reader is urged to compare the results of the two studies on the same system. None of these techniques is likely to develop so as to permit one to evaluate equilibrium constants in a polydisperse system. The ultracentrifuge is able to distinguish between monodisperse and polydisperse solutes. The light-scattering method does not give as clear a distinction between the two. Both are applicable in the range of concentration of 2-200mM total metal ion. The light-scattering method is easily adapted to measuring rates at which aggregation reactions take place. Structure Determination. L e v y and co-workers have shown that it is possible to elucidate the structure of solute isopolyions (22) in those cases where the hydrolysis product is essentially monodisperse and soluble enough to permit preparation of 2 - 4 M solutions, using x-ray diffraction. Nuclear Magnetic Resonance. Taube (18) has shown that two different chemical shifts in the 0 N M R spectrum of C r 0 ~ solutions are observed, in the approximate ratio of non-bridging O to bridging O. However, 2 M solutions of dichromate were used in water enriched to 1.4% H 0 , and no shifts were observed in several other cases studied. 1 7

2

2

7

2

1 7

Coagulation Effects. Matijevic and co-workers have shown that in optimum cases the effect of hydrolyzed metal ions upon the coagulation and reversal of charge of lyophobic colloids can be useful in identifying


188

EQUILIBRIUM

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WATER

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the hydrolyzed metal ion species (25). The same group has made the point that the critical coagulation concentrations ( c.c.c. ) are based upon the amounts of electrolyte added and that at the low concentrations necessary for highly charged ions, appreciable percentages of the electrolyte may be adsorbed on the colloid surface (26). If this is true, the actual values of c.c.c. may be much less than supposed. Furthermore, the actual solubilization and reversal of charge on the colloid takes place at concentrations only slightly greater than c.c.c. A limiting feature of this method is that it yields useful data on hydrolyzed metal ions only at concentrations well below 0.001M. Examples of Techniques Used Pb(II) Ion Hydrolysis. Below p H 8 there is general agreement upon the detailed solution chemical behavior of P b ( I I ) in Perchlorate media. Olin (31), using Potentiometrie titration, has proposed the following series of equilibria and constants, all in 3 M N a C 1 0 . 4

Pb + H O H — 4 Pb + 4 H O H = 3 Pb + 4 H O H — 6 Pb + 8 H O H = 2+

2 +

2+

2+

[Pb(OH)] + H K — [Pb (OH) ] + 4 H K [Pb (OH) ] + 4 H K [Pb (OH) ] + 8 H K +

4

3

u

+

2 +

4

6

+

4 +

4

+

4 +

8

4 4

M

+

6 8

1.26 X = 5.6 — 1.35 — 7.2

10" X 10' X HT X 10" 8

20

28 48

In the 0.1-1M total P b ( I I ) region the important solute species are P b , [ P b ( O H ) ] , and [ P b « ( O H ) ] . Furthermore, it is possible to calculate the concentrations of the several solute species present for a given set of conditions. For example, consider solutions of P b and 2 C 1 0 " to which sufficient base has been added so that the average number of O H " ions bound per P b (hydroxyl number) is 1.00. Using Olin's constants, the fractions of total P b ( I I ) existing in the different solute species are calculated for three total P b ( I I ) concentrations in Table I. 2+

4

4

4 +

8

4+

2+

4

2+

Table I.

Fraction of Total Pb(II) Existing as Different Species

Total Pb(II) molarity

Pb

0.100 0.010 0.001

0.08 0.13 0.19

2+

a

[Pb(OH)Y [Pb,(OH),y 0.003 0.81 0.02 0.64 0.08 0.30

+

[PbJOHW 0.02 0.09 0.28

{Pb (OH) y 6

8

0.10 0.21 0.21

" p H 7 assumed for this concentration.

Obviously at higher than 0.10M P b ( I I ) the solute is essentially [ P b ( O H ) ] , for hydroxyl number 1.00 solutions. Both the lightscattering (16) and the ultracentrifugation (10) techniques confirm this. 4

4

4 +


8.

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189


As a matter of fact the structure of the isopolycation has been reported by Esval (11 ) as shown i n Figure 1. A t low hydroxyl numbers O l i n (32) subsequently agrees with the earlier findings of Faucherre (12) that [ P b ( O H ) ] species are necessary to explain the Potentiometrie titration data. 3 +


2

E. 0. Esval, Ph.D. Thesis

Figure 1. Model of Polymeric Unit [Pb (OH) J '. Lead atoms are designated by small circles. Large circles represent assumed positions for oxygen atoms (11) h

;

44

Bismuth Ion Hydrolysis. In the hydroxyl number range of 0.00-2.00, there is general agreement that the important B i ( I I I ) species i n Perchlorate media are B i and [ B i ; ( O H ) ] ions. F o r the equilibrium 6 B P + 12 H O H = [ B i « ( O H ) ] + 12 H , O l i n (30) reports log K G , i 2 = 0.33 i n 3 M Perchlorate whereas Tobias (41 ) finds log K « . = —0.53 i n I M Perchlorate. Solutions i n which the hydroxyl number approaches 2.0 show hexameric bismuth cations by both ultracentrifugation (17) and light scattering (44). The structure of the isopolycation has been determined by L e v y and co-workers (22). It has cubic symmetry, the six bismuth atoms occupying the centers of the faces of an imaginary cube, with the oxygen atoms lying at the midpoints of the 12 edges. 3 +

(

1 2

1 2

f i +

0 +

+

] 2

Important Variables pH. Unfortunately it is rarely possible to prepare solutions of a given cation or metallate ion and vary p H conditions carefully over all the important p H ranges. Thus, i n the bismuth studies as the hydroxyl


190

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number is raised above 2.0 (the p H being raised), heterogeneous phases separate. Furthermore, precision of p H measurement is not yet good enough to use the Potentiometrie technique for solutions of hydrolyzing species at total metal ion concentration below ca. 10~ M. Solution Medium. It is desirable to carry out most physical measurements in 1 - 3 M N a C 1 0 in order to minimize two complications. First, activity coefficients of the hydrolyzed ionic species w i l l not be subject to significant fluctuations in a medium of high, constant, ionic strength. Second, the anion Perchlorate is thought to have insignificant ability to coordinate to the metal ions. Of course, an equilibrium constant involving highly charged ionic species might be expected to be a function of ionic strength, the more highly charged species being favored by the medium of higher ionic strength. Such seems to be the case among the few systems for which data are available at two or more ionic strengths (and the same supporting electrolyte). Thus, O l i n (31) reported two sets of constants for the P b ( I I ) hydrolysis system, the differences being in the expected direction. Tobias' constant (41) for [ B i ( O H ) ] in 1 M C 1 0 " is smaller than Olin's constant (30) by almost a factor of 10 for the same system at 3 M C10 ~. In their study of the Fe (III) hydrolysis, spectrophotometrically, at low hydroxyl numbers, M i l b u r n and Vosburgh (28) included a fairly extensive investigation of the effect of ionic strength upon equilibrium constants. For the reaction F e + H O H ± 5 [ F e ( O H ) ] - + H \ K , . ! = 2.89 X 10" at ,* = 0.10; K = 1.28 X 10" at p — 3.0. For the reaction 2 [ F e ( O H ) ] ±? [ F e ( O H ) ] , K — 170 at fx = 0.10 and 1600 at n = 3.0. In each equilibrium, the species with higher charge is favored by the medium of higher ionic strength, and a value of K = 30 at ^ = 0 was obtained by extrapolation. 3


4

6

l 2

6 +

4

4

3+

+

3

3

lA

2 +

2

2

4 +

d

d

Temperature and Time. It is my opinion that these two variables are of the utmost importance in any consideration of the hydrolytic behavior of metal cations and metallate anions. Furthermore, as yet it is impossible to separate the two variables in all cases. The reasons for these two statements w i l l become apparent by considering several specific cases. A N T I M O N Y ( V ) . In a series of papers, Lefebvre and Maria (21) have shown that the hydrolysis of Sb(OH) * 8 H 0 i n an indifferent electrolyte, the situation is even less well-defined. Some years ago it was found that solutions of Z r ( I V ) i n Cl~ media at hydroxyl number of 2.5 underwent a 3 0 % increase i n turbidity on standing at 25 °C. for one year (37). In the same series of experiments solutions of Z r O C l * 8 H 0 i n pure water exhibited a 10-fold increase i n turbidity upon refluxing for 4 hours and deposited a heterogeneous phase upon refluxing for an additional 2 hours. More recently a detailed study of the behavior of H f ( I V ) solutions i n CI" media was undertaken. A n example of what was found is shown in Figure 2. The reciprocal of the degree


+

2

2

2

T

,

,

0.05-M

Hf(BZ)

1

time - hours

Figure 2. Reciprocal of the degree of aggregation of solute hafnium species vs. time


192

EQUILIBRIUM CONCEPTS I N N A T U R A L W A T E R SYSTEMS

of aggregation of H f ( I V ) vs. time is plotted. The particular solution is 0.05M H f (made up from H f O C L • 8 H 0 , no acid added) and N a C l added to make [Cl~] = 1.0M. T w o separate phenomena or a combination of the two are likely explanations. First, the temperature coefficient of the equilibrium constants can be such as to make much larger aggregates important at higher temperatures. The second possibility is that even at room temperature the solutions are unstable with respect to larger aggregates and that the half-time of approach to equilibrium is of the order of magnitude of years, perhaps many years. The second explanation is strengthened somewhat by the fact that the solutions at 75°C. retain their turbidity upon cooling to 25 °C. for some months.


2

T U N G S T E N . W h e n the normal tungstate is hydrolyzed by adding strong acid to a H / W 0 " ratio of 1.5, it is considered that the tungstencontaining species is essentially monodisperse dodecatungstate (4, 8). However, important time effects were discovered by the fact that the Aveston (4) study was done at 5 0 ° C , whereas the light-scattering study (8) was undertaken initially at 25°C. Solutions prepared at 25°C. obviously contain larger solute species, as yet unidentified, which are quite long-lived. Only after heating at 50 °C. for 6 days do the solutions "appear" to have reached equilibrium. At the same time, solutions of W 0 " which are acidified to the same H / W 0 " ratio with buffers of acetic acid contain none of the larger, unidentified species ( Figure 3 ). +

4

2

4

+

4

2

2

0.08

1

Ni z

0.06

0.05

m

1

0.10

0.15 Inorganic Chemistry

Figure 3. Reciprocal of degree of aggregation of solute tungstate species vs. total tungsten molarity: A , z' = 0; O , z' = -0.2; •, z' = -0.4; , after heating to 50°C; , 25°C. solutions

A L U M I N U M . Matijevic and Tezak (27) found that solutions of A l in 10" to 10" M range were unstable ( unless acid is added ) and that such solutions age unpredictably with time. They can be artificially aged by heating to 9 0 ° C , producing rather large polymeric cations which are difficult to return to simple A l with acid at room temperature. A t 10" to 10" M concentration the author and co-workers are currently engaged a +

4

r,

; î +

S


1

8.

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193


in studying the behavior of A l as p H is increased and A l ( O H ) ~ as p H is lowered. In the acid solutions up to hydroxyl number 2.0 i n the temperature range 2 5 ° - 7 5 ° C . no time effect has been observed—i.e., equilibrium is approached rapidly. O n the other hand, at hydroxyl numbers in the range 2.25-2.40 instability is noted, and unpredictability is all that can be reported now. Occasionally a solution can be prepared for study. Alternatively the replication of the attempt to prepare the solution results i n a gel.


3 +

4

G A L L I U M . In the earlier quoted study of gallium hydrolysis ( 3 6 ) , solutions at hydroxyl number 1.5 deposited small amounts of precipitate in days, those at hydroxyl number 1.75 i n 2 weeks, those at hydroxyl number 2.00 in 4 months. Certainly the results reported cannot at all represent the equilibrium state. History of the Solution. From the foregoing it follows that the measurements made on a solution may reflect its history a great deal, thus accounting for the inability of different workers to agree upon details in certain cases. A solution at room temperature may contain highly aggregated isopolyions as the result of a previous history of heating or if parts of it have been subjected to localized, large fluctuations i n p H . Even less obvious differences in history can be important. Lefebvre (21 ) finds an appreciable difference in the behavior of isopolyantimonates in N a media on the one hand and in ( C H ) N media on the other. Walmsley (45) reports that the order of adding reagents in preparing solutions of isopolymolybdates greatly affects the time required for the solutions to come to equilibrium. +

3

4

+

Extrapolation to Natural Water Chemistry The chemistry of the several elements, as it occurs in natural aqueous systems, has begun to recognize some of the above-mentioned physical chemical studies, most of which have been made under carefully controlled conditions. There seem to be two important features of natural water chemistry. The first is almost always true—i.e., that the p H is in the range of 6.5-8.0. The second, perhaps not so general, is that the concentrations of elements is quite low, 10" M. A third factor of almost equal importance is that nature does not provide solutions of one or even just a few elements. For example, most natural waters w i l l contain dissolved C 0 and 0 . Thus, in extrapolating to natural water conditions the foregoing findings on P b , one would predict that at 10" M P b w i l l be the predominant species below p H 7. However, in the presence of dissolved C 0 , carbonates of lead precipitate, and all of the results quoted above for the P b system at high hydroxyl number have been 6

2

2

2+

6

2

2 +


2 +


194

EQUILIBRIUM CONCEPTS I N N A T U R A L W A T E R SYSTEMS

obtained only by rigorously excluding CO2. Lastly, it w i l l be difficult to ascertain i n detail the previous history of natural water solutions. In general one is justified in saying that for cationic systems, the higher the p H (going toward natural water), the larger w i l l be the isopolycations formed. (The reverse is true for anionic aggregation.) O n the other hand, the lower the concentration, the more important monomers w i l l be. However, it is just now becoming apparent that the higher the p H , the longer it takes for the system to come to equilibrium. It is not beyond the realm of possibility for some systems i n natural water to approach equilibrium with half-times of 10" years. Both high dilution and proximity to neutrality ( i n the sense of p H ) appear to lengthen the half-time. Such slow processes are almost certainly responsible for natural opal growth (38). Rubin (35) has found that at natural water concentration levels the precipitate flotation and ion flotation behavior of certain elements can be interpreted i n terms of isopolycation species. Possibly, many inorganic solutes have not had time to come to equilibrium, and thus nonequilibrium—i.e., kinetic—models might well be considered for natural water systems. Even biochemical chelating agents may be able to remove metals as chelates only slowly from isopolyhydroxometal ions. There is every justification for using true equilibrium constants determined in the 1 0 " M range for calculations i n the 10" M range. However, I question how many true equilibrium constants are known at this time, and more importantly whether or not we are dealing with solutions at equilibrium in natural waters. 3

CÎ

Acknowledgments I wish to acknowledge gratefully the support of the Office of Naval Research, The Army Research Office ( D u r h a m ) , and the Wright A i r Development Center, which have enabled us to pursue much of our solution chemistry research in Chapel H i l l .

Literature Cited (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Anderson, J. S., Saddington, K., J. Chem. Soc. 1949, 5381. Angstadt, R. L., Tyree, S. Y., J. Inorg. Nucl. Chem. 24, 913 (1962). Ardon, M., Plane, R. A., J. Am. Chem. Soc. 81, 3197 (1959). Aveston, J., Inorg. Chem. 3, 981 (1964). Aveston, J., Johnson, J. S., Inorg. Chem. 3, 1051 (1964). Baker, L. C. W., Pope, M. T., J. Am. Chem. Soc. 82, 4176 (1960). Cartledge, G. H., J. Am. Chem. Soc. 50, 2863 (1928). Craig, H. R., Tyree, S. Y., Inorg. Chem. 4, 997 (1965). Debye, P., Naumann, R. V., J. Chem. Phys. 17, 664 (1949). Esval, O. E., Johnson, J. S., J. Phys. Chem. 69, 959 (1965). Esval, O. E., Ph.D. Dissertation, University of North Carolina, 1962. Stumm; Equilibrium Concepts in Natural Water Systems Advances in Chemistry; American Chemical Society: Washington, DC, 1967.


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